Attribute data from high quality processes can be monitored adequately by using negative binomial charts. The optimal choice for the number r of failures involved depends on the expected rate of change in failure rate during Out-of-Control. To begin with, such results have been obtained for the case of homogeneous data. But especially in health care monitoring, (groups of) patients will often show large heterogeneity. In the present paper we will present an overview of how this problem can be dealt with. Two situations occur: the underlying structure is either unknown (the overdispersion case) or known (risk adjustment feasible). An additional complication to be dealt with is the fact that in practice typically all parameters involved are unknown. Hence estimated versions of the new proposals need to be discussed as well.